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Sound pressure
Sound pressure is the local pressure deviation from the ambient (average, or equilibrium) pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water. The SI unit for sound pressure is the pascal (symbol: Pa). The instantaneous sound pressure is the deviation from the local ambient pressure p''0 caused by a sound wave at a given location and given instant in time. The effective sound pressure is the root mean square of the instantaneous sound pressure over a given interval of time (or space). In a sound wave, the complementary variable to sound pressure is the acoustic particle velocity. For small amplitudes, sound pressure and particle velocity are linearly related and their ratio is the acoustic impedance. The acoustic impedance depends on both the characteristics of the wave and the medium. The local instantaneous sound intensity is the product of the sound pressure and the acoustic particle velocity and is, therefore, a vector quantity. The sound pressure deviation ''p is : p = \frac{F}{A} \, where :F'' = force, :''A = area. The entire pressure p''total is : p_\mathrm{total} = p_0 + p \, where :''p''0 = local ambient pressure, :''p = sound pressure deviation. Sound pressure level Sound pressure level (SPL) or sound level L''p is a logarithmic measure of the rms sound pressure of a sound relative to a reference value. It is measured in decibels (dB). Sometimes variants are used such as dB (SPL), dBSPL, or dBSPL. These variants are not permitted by SI. : L_p=10 \log_{10}\left(\frac{p^2_{\mathrm }}{p^2_{\mathrm{ref}}}\right) =20 \log_{10}\left(\frac{p_{\mathrm{rms}}}{p_{\mathrm{ref}}}\right)\mbox{ dB} \, where p_{\mathrm{ref}} is the reference sound pressure and p_{\mathrm{rms}} is the rms sound pressure being measured.Sometimes reference sound pressure is denoted ''p''0, not to be confused with the (much higher) ambient pressure. The commonly used reference sound pressure in air is p_{\mathrm{ref}} = 20 µPa (rms). In underwater acoustics, the reference sound pressure is p_{\mathrm{ref}} = 1 µPa (rms). It can be useful to express sound pressure in this way when dealing with hearing, as the perceived loudness of a sound correlates roughly logarithmically to its sound pressure. ''See also Weber-Fechner law. Measuring sound pressure levels dBSPL: A measurement of sound pressure level in decibels, where 0 dBSPL is the reference to the threshold of hearing. Often the calibration is done for 1 pascal is equal to 94 dBSPL. When making measurements in air (and other gases), SPL is almost always expressed in decibels compared to a reference sound pressure of 20 µPa, which is usually considered the threshold of human hearing (roughly the sound of a mosquito flying 3 m away). Thus, most measurements of audio equipment will be made relative to this level. However, in other media, such as underwater, a reference level of 1 µPa is more often used.C. L. Morfey, Dictionary of Acoustics (Academic Press, San Diego, 2001). These references are defined in ANSI S1.1-1994.Glossary of Noise Terms — Sound pressure level definition In general, it is necessary to know the reference level when comparing measurements of SPL. The unit dB (SPL) is often abbreviated to just "dB", which gives some the erroneous notion that a dB is an absolute unit by itself. The human ear is a sound pressure sensitive detector. It does not have a flat spectral response, so the sound pressure is often frequency weighted such that the measured level will match the perceived level. When weighted in this way the measurement is referred to as a sound level. The International Electrotechnical Commission (IEC) has defined several weighting schemes. A-weighting attempts to match the response of the human ear to pure tones, while C-weighting is used to measure peak sound levels.Glossary of Terms — Cirrus Research plc. If the (unweighted) SPL is desired, many instruments allow a "flat" or unweighted measurement to be made. See also Weighting filter. When measuring the sound created by an object, it is important to measure the distance from the object as well, since the SPL decreases in distance from a point source with 1/''r'' (and not with 1/''r''2, like sound intensity). It often varies in direction from the source, as well, so many measurements may be necessary, depending on the situation. An obvious example of a source that varies in level in different directions is a bullhorn. Sound pressure p'' in N/m² or Pa is : p = Zv = \frac{J}{v} = \sqrt{JZ} \, where : ''Z is acoustic impedance, sound impedance, or characteristic impedance, in Pa·s/m : v'' is particle velocity in m/s : ''J is acoustic intensity or sound intensity, in W/m2 Sound pressure p'' is connected to 'particle displacement' (or particle amplitude) ξ, in m, by : \xi = \frac{v}{2 \pi f} = \frac{v}{\omega} = \frac{p}{Z \omega} = \frac{p}{ 2 \pi f Z} \, . Sound pressure ''p is : p = \rho c \omega \xi = Z \omega \xi = { 2 \pi f \xi Z} = \frac{a Z}{\omega} = c \sqrt{\rho E} = \sqrt{\frac{P_{ac} Z}{A}} \, , normally in units of N/m² = Pa. where: The distance law for the sound pressure p'' is inverse-proportional to the distance ''r of a punctual sound source. : p \propto \frac{1}{r} \, (proportional) : \frac{p_1} {p_2} = \frac{r_2}{r_1} \, : p_1 = p_{2} \cdot r_{2} \cdot \frac{1}{r_1} \, The assumption of 1/''r''² with the square is here wrong. That is only correct for sound intensity. Note: The often used term "intensity of sound pressure" is not correct. Use "magnitude", "strength", "amplitude", or "level" instead. "Sound intensity" is sound power per unit area, while "pressure" is a measure of force per unit area. Intensity is not equivalent to pressure. : I \sim {p^2} \sim \dfrac{1}{r^2} \, Hence p \sim \dfrac{1}{r} \, Examples of sound pressure and sound pressure levels The formula for the sum of the sound pressure levels of n'' incoherent radiating sources is : L_\Sigma = 10\,\cdot\,{\rm log}_{10} \left(\frac{p^2_1 + p^2_2 + \cdots + p^2_n}{p^2_{\mathrm{ref}}}\right) = 10\,\cdot\,{\rm log}_{10} \left(\left({\frac{p_1}{p_{\mathrm{ref}}}}\right)^2 + \left({\frac{p_2}{p_{\mathrm{ref}}}}\right)^2 + \cdots + \left({\frac{p_n}{p_{\mathrm{ref}}}}\right)^2\right) From the formula of the sound pressure level we find : \left({\frac{p_i}{p_{\mathrm{ref}}}}\right)^2 = 10^{\frac{L_i}{10}},\qquad i=1,2,\cdots,n This inserted in the formula for the sound pressure level to calculate the sum level shows : L_\Sigma = 10\,\cdot\,{\rm log}_{10} \left(10^{\frac{L_1}{10}} + 10^{\frac{L_2}{10}} + \cdots + 10^{\frac{L_n}{10}} \right)\,{\rm dB} Loudest sounds Sound pressure levels above 194 dB at sea level produce waveforms that are distorted. Sound waves are made up of rarefaction and compression cycles but when the compression half of the wave cycle is double normal atmospheric pressure and the rarefaction half of the cycle reaches perfect vacuum (no further air molecules to remove) then the only possible increase in sound level can be achieved on the compression side of the waveform. The rarefaction half of the cycle will be clipped at any level above 194 dB. Examples of such an occurrence are large-scale manned rocket launches, sonic booms, munitions explosions, thunder, earthquakes and volcanic explosions.[http://www.makeitlouder.com/Decibel%20Level%20Chart.txt William Hamby (2004) ''Ultimate Sound Pressure Level Decibel Table] See also *Decibel, especially [[Decibel#Acoustics|the Acoustics section]] *Sone *Loudness *Weber-Fechner law (The case of Sound) *Stevens' power law *Sound power level *Amplitude *Acoustics Notes and References *Beranek, Leo L, "Acoustics" (1993) Acoustical Society of America. ISBN 0-88318-494-X *Morfey, Christopher L, "Dictionary of Acoustics" (2001) Academic Press, San Diego. External links *Conversion of sound pressure to sound pressure level and vice versa *The level of sound is dB *Table of Sound Levels - Corresponding Sound Pressure and Sound Intensity *SPL of many different sounds - txt *Ohm's law as acoustic equivalent - calculations *Definition of sound pressure level *A table of SPL values *Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf *Another Sound Pressure Level Decibel Table *Sound pressure and sound power - two commonly confused characteristics of sound Category:Sound measurements Category:Auditory perception Category:Psychophysics